Baskets of this type are used particularly in cryogenic containers or cryopreservers for the storage at very low temperature, in a cryogenic fluid, of biological products. The locking means are usually constituted by a rod threadable into a series of aligned holes formed in the transverse dividers so as to extend like a bolt in front of the forward surfaces of the drawers disposed in the basket. This arrangement has drawbacks with regard to the transverse dividers bridging the access face, of having to provide perfectly aligned holes and of presenting difficulties of threading the rod into the different holes, particularly in the lowermost transverse dividers of the basket. There has also been proposed individual locking means for each basket, constituted by a handle swingably mounted by its ends in the side walls of the box and displaceable between a lower position, in which the handle stands in front of the front face of a drawer and a raised position freeing the drawer for passage through the access face. This arrangement however has the drawback of not having any stable or blocked position in the locked or unlocked position and so occupying both hands of the user.